Flux Concentrator Core Geometry Lab

How this is built, and its real limit: the toroid's mean circumference is split by a single coverage fraction, and the saturation current is the primary current at which the core reaches B_sat. Two first-order pictures are compared and the one giving flux the easier path wins. For a closed ring or a small gap, a series reluctance network — core plus gap — is accurate, using the same engine as the Transformer Core & Magnetic Circuit Designer. Once most of the loop is open, that picture fails: the field no longer squeezes through a core-sized air tube but spreads through space. There the open arc is treated as a finite high-permeability rod sitting in the conductor's own field, whose ends limit how much it can concentrate that field (its demagnetizing factor, from the standard prolate-spheroid approximation). Both are hand calculations, good to perhaps a factor of two for the open shapes; the source paper used full 3D finite-element simulation for exactly this reason, so read the numbers as the right order of magnitude and trend, not a design figure.